Questions:

1. Write a propositional logic statement for each of the following sentences. Your propositional logic statement should be evaluated to true in the world where the sentence is true.
   Make your propositional logic symbols meaningful, otherwise you need to provide explanation about what each symbol stands for to improve the readability of your statements.
   1. It is raining outside.
   2. It is either raining or sunny outside, but not both.
   3. It is raining outside, and the ground is wet.
   4. When the ground is not wet, it is not raining.
   5. In a place called Minoma, when it feels hot and wet, the weather always changes to rain.
   
   
2. Given the following knowledge base KB:

   The only product a customer can buy from a store called T-Elephant are custom made T-shirts. John always buys gifts for his friends from T-Elephant. Jane is John's friend, and keeps (therefore owns) every gift given to her by John. John just gave Jane a gift (for Jane's birthday, maybe).

   and a claim Q = "Jane owns a T-shirt".
   
   1. Express the knowledge base KB and the claim Q using first order logic sentences that are suitable to be used in inference using lifted (generalized) Modus Ponens.
      Clearly identify the constant symbols (including the Skolem constant symbols if there is any), predicate symbols and function symbols (if there is any) used in your sentences. All the symbols not explicitly identified are assumed to be universally quantified variables.
      If the interpretation of the symbols is not conventionally obvious, clearly explain the interpretation associated with the symbols.
   2. Does KB entail Q? Prove your answer using either lifted (generalized) forward chaining or backward chaining.
   
   
3. Find the Most General Unifier to unify each of the following pairs of first order logic sentences, assuming that P is a predicate symbol and F is a function symbol; strings in quotation marks are constants, and only these strings are constants; all variables are universally quantified; and variable with the same name in the same sentence is the same variable.
   If any pair can not be unified, explain why.
   1. P(x, y, 'D') and P('A', 'B', 'C')
   2. P(x, y, F(x, y)) and P(F('A', 'B'), 'B', z)
   3. P('A', 'B', 'C') and P(F(x, y), z, 'C')
   4. P(F(x, y), F(x, 'A'), F(x, x)) and P(F('A', 'B'), z, z)
   5. P(x, x, 'C') and P(F('A', 'B'), F(y, z), 'C')
   
   
4. A training dataset contains 1000 data items. The target class label of each data item can take on one of the three values: +(positive), -(negative) or n(neutral).
   Among these 1000 data items in the training dataset, there are 370 items with the class label +, 290 items with the class label n and 340 items with the class label -.
   1. How do we calculate the entropy of the above given training dataset? What does this entropy mean?
   2. The data items have a description attribute A. Based on each item's value of its attribute A, the given dataset is divide into two subsets, subset I and subset II.
      Subset I contains 485 data items, where 195 of them have the class label + and 290 of them have the class label n. Subset II contains 515 data items, where 175 of them have the class label + and 340 of them have the class label -.
      How do we calculate the information gain of attribute A?
   3. In the whole process of building a decision tree, why do we never calculate the information gain of the target attribute (the class label)?
   
   
5. Given the following partial order plan (where clearly S is the start step and F is the final step) with numbers in the boxes indicating the duration of the steps, determine the earliest possible start time and the latest possible start time of each step, and list the steps in the critical path of the plan.
   

What and How to Submit

You can hand in a hard copy before the due date/time.

Alternatively, you can upload your assignment file (.pdf or .txt) to VIU Learn, under CSCI 485's assessment/assignments/A5 tab.

Or, you can submit your assignment file (.pdf or .txt only) on any cub/pup machine using the following command in the directory where your assignment file is:
~liuh/bin/submit 485 A5 .